Thermodynamic Description of the Ag-Pb-Te Ternary System

Gierlotka, Wojciech; Łapsa, Joanna; Fitzner, K.

doi:10.1007/s11669-010-9791-8

Cited by 17 publications

(12 citation statements)

References 23 publications

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“…The thermodynamic models employed in this work are based on previous assessments by Gierlotka et al [12,31] on the Pb-Te system. In these expressions, the Gibbs energies G ϕ m of each phase ϕ taking part in the equilibria are defined using the models described below.…”

Section: Thermodynamic Models For the Calphad Methodsmentioning

confidence: 99%

“…Thus, following Ref. [31], in this work we have also used the associate model [36] to describe this phase. In CALPHAD terminology, the term "associate" is used to denote an association between unlike atoms when the attractive forces between the atoms are not strong enough to form a stable chemical molecule.…”

Section: Liquidmentioning

confidence: 99%

“…(Pb, Te) 1 :(Te, Pb) 1 . In a later publication [31], the PbTe phase was assumed to be an ideal defect-free compound. From our DFT calculations in this work, we found that the Fermi level is positioned where vacancy defects have the lowest formation energy, and are thus more stable than the anti-site defects on both the Pb and Te sublattices, i.e.…”

Section: Modification and Assessment Of The Calphad Modelmentioning

confidence: 99%

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Ab initio study of intrinsic point defects in PbTe: an insight into phase stability

et al. 2015

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The stability of intrinsic point defects in PbTe, one of the most widely studied and efficient thermoelectric material, is explored by means of Density Functional Theory (DFT). The origin of nand p-type conductivity in PbTe is attributed to particular intrinsic charged defects by calculating their formation energies. These DFT calculated defect formation energies are then used in the Gibbs free energy description of this phase as part of the Pb-Te thermodynamic model built using the CALPHAD method, and in the resulting phase diagram it is found that its solubility lines and non-stoichiometric range agree very well with experimental data. Such an approach of using DFT in conjunction with CALPHAD for compound semiconductor phases that exhibit very small ranges of non-stoichiometry does not only make the process of calculating phase diagrams for such systems more physical, but is necessary and critical for the assessment of unknown phase diagrams.

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Section: Thermodynamic Models For the Calphad Methodsmentioning

confidence: 99%

Section: Liquidmentioning

confidence: 99%

Section: Modification and Assessment Of The Calphad Modelmentioning

confidence: 99%

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Ab initio study of intrinsic point defects in PbTe: an insight into phase stability

et al. 2015

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“… The integral mixing enthalpy of liquid Ag-Mg-Pb alloys at 1116 K, for the following intersections: (a)—Series A (Mg 0.25 Pb 0.75 ) 1−x Ag x —blue line: data calculated with Equation (4), blue diamonds—experimental data; (b)—Series B (Mg 0.50 Pb 0.50 ) 1−x Ag x —green line: data calculated with Equation (4), green circles—experimental data; (c)—Series C (Mg 0.75 Pb 0.25 ) 1−x Ag x —red line: data calculated with Equation (4), red rectangles—experimental data. The purple dash line is the integral molar mixing enthalpy of Ag–Mg [ 10 ] liquid alloys, and the brown dash-dot line is the integral molar mixing enthalpy of Ag–Pb [ 17 ] liquid alloys. …”

Section: Figurementioning

confidence: 99%

“…The Ag–Pb phase diagram is a simple eutectic system and has been widely investigated [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. A detailed review can be found in [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

Mixing Enthalpies of Liquid Ag–Mg–Pb Alloys: Experiment vs. Thermodynamic Modeling

et al. 2022

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A drop calorimetric method was used to measure liquid Ag–Mg–Pb alloys. The partial and integral mixing enthalpies of the investigated alloys were determined at a temperature of 1116 K. The experiments were performed for four separate series starting from binary alloys with a constant xMg/xPb ratio of 1/3, 1, 3 ((Mg0.25Pb0.75)1−xAgx, (Mg0.50Pb0.50)1−xAgx, (Mg0.75Pb0.25)1−xAgx) and xAg/xMg ratio of 1/3 (Ag0.25Mg0.75)1−xPbx. Next, the ternary interaction parameters were determined using the Muggianu model, the thermodynamic properties of binary systems in the form of the Redlich-Kister equations and the values of the mixing enthalpy changes, which were determined in this study. The partial mixing enthalpies of Ag, Mg, and Pb were calculated based on the binary and elaborated ternary interaction parameters for the same intersections in which the measurements were conducted. It was found that the ternary Ag-Mg-Pb liquid solutions are characterized by negative deviations from the ideal solutions, with a maximal value slightly lower than –13 kJ/mol for alloys with the ratio (Mg0.75Pb0.25) and xAg = 0.4166.

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Modeling Charged Defects Using the Defect Energy Formalism With a Charge Sublattice Within a CALPHAD Framework

Adekoya,

Snyder

2024

Adv Funct Materials

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The non‐stoichiometry of material compounds significantly influences their functional properties. In semiconductors, point defects determine whether a material is n‐type or p‐type and the concentration of charge carriers. Even in structural alloys and ion conductors used in batteries and fuel cells, non‐stoichiometry and dilute defects play an integral role in their function. The design of metal alloys has advanced rapidly with the aid of thermodynamic modeling using calculation of phase diagrams (CALPHAD) to predict the phases produced during different processing conditions. While thermodynamic modeling has been done previously by fitting experimental data, the advent of first‐principle techniques has enabled the computational prediction of material properties. The defect energy formalism (DEF) is described for modeling charged and uncharged defects in compounds, showing that it accurately predicts non‐stoichiometry using density functional theory (DFT), without fitting experiments. The model reproduces the expected defect and free‐charge carrier concentrations using the statistical mechanics approach commonly used in most DFT defect studies. Finally, the model is used to accurately predict the single‐phase region of PbTe with no fitting to measured defect concentrations. This method can revolutionize materials development of insulators, semiconductors, and even metals by allowing rapid DFT calculations to replace laborious experiments when dilute defects are involved.

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Thermodynamic Description of the Ag-Pb-Te Ternary System

Cited by 17 publications

References 23 publications

Ab initio study of intrinsic point defects in PbTe: an insight into phase stability

Ab initio study of intrinsic point defects in PbTe: an insight into phase stability

Mixing Enthalpies of Liquid Ag–Mg–Pb Alloys: Experiment vs. Thermodynamic Modeling

Modeling Charged Defects Using the Defect Energy Formalism With a Charge Sublattice Within a CALPHAD Framework

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